# Thread: Help with simplifying?

1. ## Help with simplifying?

Rational Equations?

2. EDIT : I didn't see you posted an image, sorry. But it seems that the link is dead. Can you upload it again ?

3. Originally Posted by Bacterius
EDIT : I didn't see you posted an image, sorry. But it seems that the link is dead. Can you upload it again ?
I fixed it.

4. They are not equations but expressions

For the first one, put them under common denominator (multiply top and bottom of each fraction by the denominator of the other), then factorize. You should find something that simplifies ... look :

$\frac{5}{x + 3} - \frac{x + 2}{x^2 + 4x + 3}$

Factorize the quadratic expression to make it easier first :

$\frac{5}{x + 3} - \frac{x + 2}{(x + 3)(x + 1)}$

Now put under common denominator :

$\frac{5(x + 3)(x + 1)}{(x + 3)(x + 3)(x + 1)} - \frac{(x + 3)(x + 2)}{(x + 3)(x + 3)(x + 1)}$

So it becomes :

$\frac{5(x + 3)(x + 1) - (x + 3)(x + 2)}{(x + 3)(x + 3)(x + 1)}$

Note you can factor out the $(x + 3)$ on the top of the fraction :

$\frac{(x + 3)[5(x + 1) - (x + 2)]}{(x + 3)(x + 3)(x + 1)}$

You can cancel it out :

$\frac{5(x + 1) - (x + 2)}{(x + 3)(x + 1)}$

There may be further simplification possible, though ...

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For the second one, you can factor out $y^{15}$ on the top of the fraction, then cancel out :

$\frac{y^{60} + y^{45}}{y^{15}}$

Factor out :

$\frac{y^{15}(y^{45} + y^{30})}{y^{15}}$

Simplify :

$y^{45} + y^{30}$ with $y \neq 0$ (keep the domain of the original expression)